Evaluate the following determinant:
$$ det \left( \begin{matrix}1&2&-3&1\\2&-1&-1&2\\1&2&2&-1\\1&3&-3&-1\end{matrix} \right) $$

Answer

$$ det \left( \begin{matrix}1&2&-3&1\\2&-1&-1&2\\1&2&2&-1\\1&3&-3&-1\end{matrix} \right) = 40 $$

Explanation

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Evaluate the following determinant: $$ det \left( \begin{matrix}1&2&-3&1\\2&-1&-1&2\\1&2&2&-1\\1&3&-3&-1\end{matrix} \right) $$

$$ det \left( \begin{matrix}1&2&-3&1\\2&-1&-1&2\\1&2&2&-1\\1&3&-3&-1\end{matrix} \right) = 40 $$

Evaluate the following determinant:
$$ det \left( \begin{matrix}1&2&-3&1\\2&-1&-1&2\\1&2&2&-1\\1&3&-3&-1\end{matrix} \right) $$